Converter of signed binary two's complement: converting to decimal system (base ten) integer numbers

Convert signed binary two's complement numbers to decimal system (base ten) integers

Entered binary number length must be: 2, 4, 8, 16, 32, or 64 - otherwise extra bits on 0 will be added in front (to the left).

How to convert a signed binary number in two's complement representation to an integer in base ten:

1) In a signed binary two's complement, first bit (leftmost) indicates the sign, 1 = negative, 0 = positive.

2) Get the signed binary representation in one's complement, subtract 1 from the initial number.

3) Construct the unsigned binary number: flip all the bits in the signed binary one's complement representation (reversing the digits) - replace the bits set on 1 with 0s and the bits on 0 with 1s.

4) Multiply each bit of the binary number by its corresponding power of 2 that its place value represents.

5) Add all the terms up to get the positive integer number in base ten.

6) Adjust the sign of the integer number by the first bit of the initial binary number.

Latest binary numbers in two's complement representation converted to signed integers in decimal system (base ten)

1110 0100 1001 0010 0100 0000 0000 0000 = -460,177,408 Sep 23 10:46 UTC (GMT)
1111 1001 1111 0010 = -1,550 Sep 23 10:45 UTC (GMT)
1110 1001 = -23 Sep 23 10:45 UTC (GMT)
1010 1010 1111 1010 1000 0001 0101 1111 = -1,426,423,457 Sep 23 10:45 UTC (GMT)
0000 1010 = 10 Sep 23 10:45 UTC (GMT)
1111 1111 1111 1111 1111 1111 1111 1010 = -6 Sep 23 10:42 UTC (GMT)
0110 1011 = 107 Sep 23 10:41 UTC (GMT)
1110 0011 = -29 Sep 23 10:38 UTC (GMT)
1101 1001 = -39 Sep 23 10:38 UTC (GMT)
0100 0001 = 65 Sep 23 10:38 UTC (GMT)
1100 0111 = -57 Sep 23 10:24 UTC (GMT)
1100 1100 = -52 Sep 23 10:23 UTC (GMT)
1100 0111 = -57 Sep 23 10:16 UTC (GMT)
All the converted signed binary two's complement numbers

How to convert signed binary numbers in two's complement representation from binary system to decimal

To understand how to convert a signed binary number in two's complement representation from the binary system to decimal (base ten), the easiest way is to do it by an example - convert binary, 1101 1110, to base ten:

  • In a signed binary two's complement, first bit (leftmost) indicates the sign, 1 = negative, 0 = positive. The first bit is 1, so our number is negative.
  • Get the signed binary representation in one's complement, subtract 1 from the initial number:
    1101 1110 - 1 = 1101 1101
  • Get the binary representation of the positive number, flip all the bits in the signed binary one's complement representation (reversing the digits) - replace the bits set on 1 with 0s and the bits on 0 with 1s:
    !(1101 1101) = 0010 0010
  • Write bellow the positive binary number representation in base two, and above each bit that makes up the binary number write the corresponding power of 2 (numeral base) that its place value represents, starting with zero, from the right of the number (rightmost bit), walking to the left of the number, increasing each corresonding power of 2 by exactly one unit:
  • powers of 2: 7 6 5 4 3 2 1 0
    digits: 0 0 1 0 0 0 1 0
  • Build the representation of the positive number in base 10, by taking each digit of the binary number, multiplying it by the corresponding power of 2 and then adding all the terms up:

    0010 0010(2) =


    (0 × 27 + 0 × 26 + 1 × 25 + 0 × 24 + 0 × 23 + 0 × 22 + 1 × 21 + 0 × 20)(10) =


    (0 + 0 + 32 + 0 + 0 + 0 + 2 + 0)(10) =


    (32 + 2)(10) =


    34(10)

  • Signed binary number in two's complement representation, 1101 1110 = -34(10), a signed negative integer in base 10